Integrated Circuit Methods of Ring Modulation
On the C64 SID chip, ring modulation multiplies a triangle wave with a square wave.
On an ARP Odyssey synthesizer (and a few others from that era as well) the ring modulator is an XOR function (formed from two NAND gates) fed from the square wave outputs of the two oscillators. For the limited case of square or pulse wave signals, this is identical to true ring modulation.
Analog multiplier ICs (such as those made by Analog Devices) would work quite nicely as ring modulators, of course with regard to such matters as their operating limits and scale factors. Use of multplier ICs means that the modulation products are largely confined to sum and difference frequency of inputs (unless the circuit is overdriven), rather than the much more complicated products of the rectifier circuit.
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